Variable light focusing is the ability to flexibly select the focal distance of a lens. This feature presents technical challenges, but is significant for optical interrogation of three-dimensional objects. Numerous lens designs have been proposed to provide flexible light focusing, including zoom, fluid, and liquid-crystal lenses. Although these lenses are useful for macroscale applications, they have limited utility in micron-scale applications due to restricted modulation range and exacting requirements for fabrication and control. Here, we present a holographic focusing method that enables variable light focusing without any physical modification to the lens element. In this method, a scattering layer couples low-angle (transverse wave vector) components into a full angular spectrum, and a digital optical phase conjugation (DOPC) system characterizes and plays back the wavefront that focuses through the scattering layer. We demonstrate micron-scale light focusing and patterning over a wide range of focal distances of 22-51 mm. The interferometric nature of the focusing scheme also enables an aberration-free scattering lens. The proposed method provides a unique variable focusing capability for imaging thick specimens or selective photoactivation of neuronal networks.
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